Space of modular forms of level 320, weight 5, and Character 320.r

• Label: 320.5.r
• Level: $320$
• Weight: $5$
• Character orbit: 320.r
• Rep. character: $\chi_{320}(111,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(320, [\chi])\).

	Total	New	Old
Modular forms	400	64	336
Cusp forms	368	64	304
Eisenstein series	32	0	32

Trace form

64 * q + 192 * q^11 - 704 * q^19 + 2304 * q^23 - 3648 * q^27 - 1728 * q^29 + 3648 * q^37 + 5376 * q^39 - 5568 * q^43 + 21952 * q^49 - 9728 * q^51 + 960 * q^53 + 960 * q^59 + 3776 * q^61 + 18880 * q^67 - 9792 * q^69 + 19968 * q^71 + 9408 * q^77 - 46656 * q^81 - 10560 * q^83 - 11200 * q^85 - 39168 * q^91 - 17472 * q^93 + 49216 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.5.r.a	$320$	$5$	320.r	16.f	$4$	$64$	$32$	$33.078$		None			✓	✓	80.5.r.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)